Quantum criticality and incipient phase separation in the thermodynamic properties of the Hubbard model

Mott Quantum Critical Points at Finite Doping

We demonstrate that a finite-doping quantum critical point (QCP) naturally descends from the existence of a first-order Mott transition in the phase diagram of a strongly correlated material. In a prototypical case of a first-order Mott transition the surface associated with the equation of state for the homogeneous system is "folded" so that in a range of parameters stable metallic and insulating phases exist and are connected by an unstable metallic branch. Here we show that tuning the chemical potential, the zero-temperature equation of state gradually unfolds. Under general conditions, we find that the Mott transition evolves into a first-order transition between two metals, associated with a phase separation region ending in the finite-doping QCP. This scenario is here demonstrated solving a minimal multiorbital Hubbard model relevant for the iron-based superconductors, but its origin-the splitting of the atomic ground state multiplet by a small energy scale, here Hund's coupling-is much more general. A strong analogy with cuprate superconductors is traced.

Evaluating Second-Order Phase Transitions with Diagrammatic Monte Carlo: Néel Transition in the Doped Three-Dimensional Hubbard Model

Diagrammatic Monte Carlo-the technique for the numerically exact summation of all Feynman diagrams to high orders-offers a unique unbiased probe of continuous phase transitions. Being formulated directly in the thermodynamic limit, the diagrammatic series is bound to diverge and is not resummable at the transition due to the nonanalyticity of physical observables. This enables the detection of the transition with controlled error bars from an analysis of the series coefficients alone, avoiding the challenge of evaluating physical observables near the transition. We demonstrate this technique by the example of the Néel transition in the 3D Hubbard model. At half filling and higher temperatures, the method matches the accuracy of state-of-the-art finite-size techniques, but surpasses it at low temperatures and allows us to map the phase diagram in the doped regime, where finite-size techniques struggle from the fermion sign problem. At low temperatures and sufficient doping, the transition to an incommensurate spin density wave state is observed.

Structural Properties and Hopping Conduction in the Normal State of Electron-Doped Superconductor Cuprate Eu2-x Ce x CuO4+α-δ

Electron-doped superconducting cuprate of Eu_2-x Ce _x CuO_4+α-δ has been studied in the whole doping regime from x = 0.10-0.20 with reducing oxygen content to investigate the relation between the crystal structure and the hopping conduction in the normal state. Parameter of the crystal structure has been extracted from the X-ray diffraction (XRD) measurement while hopping conduction parameters have been obtained from resistivity measurements. The Eu-O bond length decreases with the increasing doping concentration, indicating the successful doping by the partial replacing of Eu³⁺ with Ce⁴⁺. The resistivity increases with decreasing temperature in all measured samples. This is an indication of bad metal-like behavior in the whole regime in the normal state of electron-doped superconducting cuprate of Eu_2-x Ce _x CuO_4+α-δ. The temperature dependence of resistivity was analyzed by the Arrhenius law and the variable range hopping model. It is found that the hopping conduction mechanism more likely follows the variable range hopping rather than the Arrhenius law, indicating that the hopping mechanism occurs in three dimensions. The Cu-O bond length probably plays an important role in decreasing the activation energy. The decreasing value of the activation energy correlates with the increase in the localization radius.

Entropy in the Non-Fermi-Liquid Regime of the Doped 2D Hubbard Model

We study thermodynamic properties of the doped Hubbard model on the square lattice in the regime of strong charge and spin fluctuations at low temperatures near the metal-to-insulator crossover and obtain results with controlled accuracy using the diagrammatic Monte Carlo method directly in the thermodynamic limit. The behavior of the entropy reveals a non-Fermi-liquid state at sufficiently high interactions near half filling: A maximum in the entropy at nonzero doping develops as the coupling strength is increased, along with an inflection point, evidencing a metal to non-Fermi-liquid crossover. The specific heat exhibits additional distinctive features of a non-Fermi-liquid state. Measurements of the entropy can, therefore, be used as a probe of the state of the system in quantum simulation experiments with ultracold atoms in optical lattices.